On the Physical Vacuum Singularity of Compressible Fluids (Huihui Zeng, Tsinghua University)

10.07.2018 14:00

The physical vacuum singularity of the sound speed being of 1/2-Holder but not Lipshitzian continuous near vacuum boundaries as a characteristic phenomenon appears in some important physical situations, such as compressible flows with frictional damping, gaseous stars, and shallow waters. Systems of PDEs of compressible fluids are highly degenerate near vacuum states of physical singularity so that the standard approach of symmetric systems developed by Friedrichs-Lax-Kato does not apply. In this talk, the global-in-time well-posedness and long time behavior of solutions to some free boundary problems of compressible fluids with the physical vacuum singularity will be discussed. The particular emphasize will be on global-in-time solutions to the compressible Euler equations with damping and their time asymptotic equivalence to the Barenblatt solution for the corresponding porous media equation via Darcy's law.

Lieu

salle 623, Séminaire d'analyse numérique

entrée libre